Two‐sample inference procedures under nonproportional hazards

Abstract

We introduce a new two‐sample inference procedure to assess the relative performance of two groups over time. Our model‐free method does not assume proportional hazards, making it suitable for scenarios where nonproportional hazards may exist. Our procedure includes a diagnostic tau plot to identify changes in hazard timing and a formal inference procedure. The tau‐based measures we develop are clinically meaningful and provide interpretable estimands to summarize the treatment effect over time. Our proposed statistic is a U‐statistic and exhibits a martingale structure, allowing us to construct confidence intervals and perform hypothesis testing. Our approach is robust with respect to the censoring distribution. We also demonstrate how our method can be applied for sensitivity analysis in scenarios with missing tail information due to insufficient follow‐up. Without censoring, Kendall's tau estimator we propose reduces to the Wilcoxon‐Mann–Whitney statistic. We evaluate our method using simulations to compare its performance with the restricted mean survival time and log‐rank statistics. We also apply our approach to data from several published oncology clinical trials where nonproportional hazards may exist.

Progression-Free Survival Analysis With a Graphical Estimand Approach in the Phase 2 SAMCO-PRODIGE 54 Trial

“…Obviously, the dRMST test and the tau-based test did not lead to the same conclusion. However, it could be noted that the PFS curves in our study were similar to case 5 (early crossing setting) considered in the simulation study conducted by Tai et al 2 In that setting, authors have shown that the tau-based test has poor power and was less powerful than the dRMST test.…”

“…Previously, we proposed a novel estimand-based measure, the tau process, to describe the treatment effect useful for NPH . Denote T l as the time to a specified end point for group l with F l ( t ) = Pr( T l ≤ t ) and S l ( t ) = Pr( T l > t ), respectively, where l = 0,1 indicate the treatment and control groups, respectively.…”

“…Prompt design is currently more of an art than a science and can be challenging, time-consuming, and costly. 2,3 In the future, automated approaches to normalizing prompts and soft prompting may alleviate some of these issues. 4,5 Methods such as developing more specialized clinical language models, linking to vetted knowledge sources, and fact-checking across different LLM instances are just a few other potential avenues to develop more factual question-answering systems.Robustness to minor alterations in prompts is a major issue for evaluating these LLMs and poses safety concerns.…”

Progression-Free Survival Analysis With a Graphical Estimand Approach in the Phase 2 SAMCO-PRODIGE 54 Trial—Reply

“…Obviously, the dRMST test and the tau-based test did not lead to the same conclusion. However, it could be noted that the PFS curves in our study were similar to case 5 (early crossing setting) considered in the simulation study conducted by Tai et al In that setting, authors have shown that the tau-based test has poor power and was less powerful than the dRMST test.…”

“…We then discussed the importance of identifying patients with deficient mismatch repair and/or microsatellite instability status and initial resistance to immunotherapy to select them for an appropriate suitable alternative treatment. In this context of delayed treatment effect, we agree that the tau process methodology proposed by Tai et al provide a useful tool to more accurately capture the timing of reversing hazards and examine treatment effects over time. However, regarding the comparison tests of survival curves, there is not a general rule to determine which method will perform better.…”